Effects of random external fields on the dynamics of the one-dimensional Blume-Capel model

The dynamical properties of quantum spin systems have received a great deal of theoretical and experimental attention in the past decades. Only recently, has much attention been paid to the random quantum spin systems. In this paper the effect of random external field on the dynamics of one-dimensional Blume-Capel model with s = 1 in the high-temperature limit is investigated by using. the recurrence relations method. The spin autocorrelation function as well as the corresponding spectral density of the system is calculated in the presence of the field that satisfies two types of distributions. When the single-ion anisotropy takes 0, for the bimodal distribution, the dynamics of the system behaves as a crossover from a central peak behavior to a collective mode one. For the Gaussian distribution, when the standard deviation is small, the dynamical behavior of the system also exhibits a crossover; when the standard deviation is large enough, the system only shows a disordered behavior. We also discuss the effect of the single-ion anisotropy on the dynamical property of the system, and find that the collective-mode behavior becomes weaker as the single-ion anisotropy exists.